Logarithmic mean value

It may be noted that using Underwood s approximation (equation 9.10), the calculated values for the mean temperature driving forces are 41.9 K and 39.3 K for counter- and co-current flow respectively, which agree exactly with the logarithmic mean values. 

The integration may be carried out only if the variation of driving force throughout the depth of the bed may be estimated. It was not possible to make measurements of the concentration profiles within the bed, although as the value of AC did not vary greatly from the inlet to the outlet, no serious error was introduced by using the logarithmic mean value AClm. 

A Cta concentration difference Logarithmic mean value of C kmol/m3 NL-3... 

To determine am experimentally only M, the wall temperature and average fluid temperature at entry and exit need to be measured. The use of the logarithmic mean value is also suggested by the following when both the wall temperature and the local heat transfer coefficient a are constant, then am = a is only true when A og is used in the definition for am. Then from (1.32) it follows that... 

Equation (11.16) calls for use of a logarithmic mean value of the U AT cross product, where the overall coefficient at one end of the exchanger is multiplied by the temperature approach at the other. The derivation of this equation requires that assumptions 2 to 4 above be accepted. 

Temperature difference, C or °F AT , between fluid and wall of finned tube AT, corrected overall average value ATp, average difference between fluid and fins AT], logarithmic mean value Fin efficiency, ATp/AT ... 

Calculate the overall heat transfer coefficient for each zone using an appropriate set of heat transfer correlations and an appropriate correlation from Table 17.32. More specifically, if a linear dependence between U and A can be assumed, an arithmetic mean between the terminal U values should be used as a mean value. If both U and T vary linearly with q, the mean U value should be calculated from a logarithmic mean value of the UAT product as indicated in Table 17.32. Next, if both 1IU and T vary linearly with q, the third equation for the mean U value from Table 17.32 should be used. Finally, if U is not a linear function of either A or q, the mean value should be assessed following the procedure described in the section starting on p. 17.47. 

The toluene permeability may be considered as a constant and the logarithmic mean value may be used for the average toluene concentration at the feed side. 

In such a case, a logarithmic mean value of S should be used. Because the inlet air contains no ammonia, the value of the abscissa in Figure 4-1 equals xj/x. The number of transfer units required can be determined from this Colburn correlation. 

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